User blog:Alejandro Magno/Googleaarex - Large Number Competition Functions
Welcome! In this post, I will list all of the notations and functions Googleaarex, me and the other users who participated in his game ''My number is bigger! (Googology Wiki Version) ''coined. Flain() Function n!! = (((...(((n!)!)!)!)...)!)!)!)! w/ n levels n!!! = (((...(((n!!)!!)!!)!!)...)!!)!!)!!)!! w/ n levels n!m = n!!!...!!! w/ m !'s Flain(n) = n!n Flain_0(n) = Flain(n) Flain_1(0) = Flain(200!200) Flain_1(n) = Flain(Flain_1(n-1)) Flain_m(0) = Flain_m-1(200!200) Flain_m(n) = Flain_m-1(Flain_m(n-1)) Arrow() Function ^ means an up arrow, and v means a down arrow. Arrow(n,m,0) = n*m Arrow(n,m,1) = n^m Arrow(n,m,2) = n^vm Arrow(n,m,3) = n^^m Arrow(n,m,4) = n^vvm Arrow(n,m,5) = n^v^m Arrow(n,m,6) = n^^vm Arrow(n,m,7) = n^^^m Arrow(n,m,8) = n^vvvm Arrow(n,m,9) = n^vv^m Arrow(n,m,10) = n^v^vm Arrow(n,m,11) = n^v^^m Arrow(n,m,12) = n^^vvm Arrow(n,m,13) = n^^v^m Arrow(n,m,14) = n^^^vm Arrow(n,m,15) = n^^^^m Arrow(n,m,16) = n^vvvvm Formula for Arrow(n,m,k), write k in binary, then replace each 1 with an up arrow, and each 0 with a down arrow. That is the expression you put between n and m. Extensions Two and 1 Entry Arrow(n,m) = Arrow(n,n,m) Arrow(n) = Arrow(n,n) ()-Notation Arrow(Arrow(10,10,10),Arrow(10,10,10),Arrow(10,10,10)) = a = (1) Arrow(Arrow(a,a,a),Arrow(a,a,a),Arrow(a,a,a)) = b = (2) Arrow(Arrow(b,b,b),Arrow(b,b,b),Arrow(b,b,b)) = c = (3) (a) = ((1)) (a+1) = ((1)1) ((1)a) = ((1)(1)) ((2)) = ((1)(1)(1)...(1)(1)(1)) w/ a (1)'s ((2)(2)) = ((2)(1)(1)(1)...(1)(1)(1)) w/ a (1)'s ((3)) = ((2)(2)(2)...(2)(2)(2)) (((1))) = ((a)) (((1)1)) = ((a+1)) (((1)(1)) = (((1)a)) (((2))) = (((1)(1)(1)...(1)(1)(1))) w/ a (1)'s ((((1)))) = (((a))) (((((1))))) = ((((a)))) Sub-extensions My Extension This is my extension: (1)2 = (((...(((a)))...))) w/ a levels (2)2 = Arrow((2)2) ((1))2 = (a)2 ((1)1)2 = Arrow(((1))2,((1))2,((1))2) ((1)(1))2= ((1)a)2 ((2))2 = ((1)(1)(1)...(1)(1)(1))2 w/ a (1)'s ... ((1)2)2 = (((...(((1)))...)))2 w/ a levels (1)3 = (((...(((1)2)2)2)...)2)2)2 w/ a levels (n)(1)= (n)a (n)(1)1 = (n)a+1 (n)(1)(1) = (n)(1)a (n)(2) = (n)(1)(1)(1)...(1)(1)(1) w/ a nestings ... (n)(m)(1) = (n)(m)a ... (1)1,2 = (a)(a)(a)(a)...(a)(a)(a) w/ a levels (1)2,2 = ((((...(((1)1,2)1,2)1,2)...)1,2)1,2)1,2 w/ a levels (1)(1),2 = (1)a,2 ... (1)(1)1,2 = (1)(1)(1)(1)(1)...(1)(1)(1) w/ a levels (1)1,3 = (1)(1)(1)...(1)(1)(1)1,2 w/ a levels ... Googleaarex Extension (1,2) = ((...((a))...))/w a ()'s inside out. (1,3) = ((...((a,2),2)...,2),2)/w a ()'s inside out. (1,1,2) = (1,(1,...(1,(1,a))...))/w a ()'s inside out. (1,1,1,2) = (1,1,(1,1,...(1,1,(1,1,a))...))/w a ()'s inside out. ... (122) = (1,1,1,...,1,1,2) w/ a entries (1,222) = (((...(((122)22)22)...)22)22)22) w/ a nestings (123) = (1,1,1,...,1,1,222) w/ a entries (121,2) = (12(12(12(...(12(12(122)))...))) w/ a nestings (12122) = (121,1,1,...,1,1,2) w/ a entries (132) = (121212...1212122) w/ a rows ... (11,22) = (1[(1[...(1[(1a2)]2)...]2)]2)/w a []'s inside out (11,32) = (1[(1[...(1[(1a,22),2]2)...,2]2),2]2)/w a []'s inside out (11,1,22) = (1[1,(1[1,...(1[1,(11,a2)]2)...]2)]2)/w a []'s inside out ... (1,22) = (1[1[...[1[1a2]2]...]2]2) w/ a nestings (2,22) = Arrow((1,22)) (1,2,22) = (((...(((1,22),22),22)...),22),22),22) w/ a nestings (1,23) = (1[1[...[1[1a2]2]...]2]2,22) (1,21,22) = (1,21[1[...[1[1a2]2]...]2]2) w/ a nestings ... (1222) = (1,21,21,2...,1,21,21,2) w/ a second level entries (1322) = (122122122...122122122) w/ a second level rows ... (1,32) = (1[1[...[1[1a2]2]...]2]22) ... SuperJedi224/Googleaarex Extension Let f(x) equal ((...(x)...)) with x sets of parentheses. Let g(x) equal f(f(...f(x)....)) with x "f"'s f() = (1)(), g() = (2)(), etc. ... Let define f(x)(y) = (((...(((x)))...)))(y) w/ x levels Let define g(x)(y) = f(f(f(...(f(f(f(x))))...))(y) w/ x levels Let define f(x)(y) = (1)(x)(y), g(x)(y) = (2)(x)(y), etc. ... f(a)(b)© = (((...(((a)))...)))(b)© /w a ()'s nested out f(a)(b)©(d) = (((...(((a)))...)))(b)©(d) /w a ()'s nested out ... (n)(m)l = (n)(m)(m)(m)...(m)(m)(m) w/ l entries (n)(m)(1) = (n)(m)a ... F Function F_0(n) = Arrow((100,100100)(100)(100)...(100)(100))/w n (100)'s F_x+1(n) = F_x(F_x(...F_x(F_x(n))...))/w n F's F_a(n) = F_an(n) F_0,1(0) = F_100(100) F_0,1(n) = F_(F_0,1(n-1))(100) F_1,1(0) = F_0,1(100) F_1,1(n) = F_0,1(F_1,1(n-1)) F_0,2(0) = F_0,100(100) F_0,2(n) = F_0,(F_0,2(n-1))(100) F_1,2(0) = F_0,2(100) F_1,2(n) = F_0,2(F_1,2(n-1)) ... ... ... If there is something i did not put in, just tell me. Category:Blog posts